Solids under stress definitions

Hooke’s law

The tension in a spring or wire is proportional to its extension

Spring constant, k

The force per unit extension

Hookes law equation

F= kx (Force= spring constant x extension)

Stress

Stress is the force per unit cross-sectional area

Strain

The extension per unit length due to an applied stress

Equation for stress

Stress= Force/ Area

Equation for strain

Strain= Extension/ length

Young’s modulus

E= Stress/ strain, or force x length/area x extension

Crystal

Solids in which atoms are arranged in a regular array. There is a long range order.

Crystalline solid

Solid consisting of a crystal or many crystals, usually arranged randomly. The latter is a polycrystalline solid. Metals are polycrystalline.

Amorphous solid

Solids which have atoms arranged randomly. There is no long range order, short range order.

Polymeric solid

A solid which is made up of chain-like molecules

Ductile material

A material that can be drawn out into a wire.

Elastic strain

This is the strain that disappears when stress is removed, so the object returns to its original shape and size

Plastic strain

Once the force is removed, the object doesn’t return to its original shape. In metal, it arises from the movement of dislocations within the crystal structure.

Elastic limit

This is the point at which deformation is now plastic

Dislocations in crystals

Certain faults in crystals which reduce the stress needed for planes of atoms to slide.

Grain boundaries

The boundaries between crystals in a polycrystalline material

Ductile fracture (necking)

The fracture of a rod or wire is preceded by thinning at the weakest point which increases stress.

Brittle fracture

A type of break that occurs in materials without significant deformation.

Work Done

E=½ fx

Hysteresis

Energy lost in a system

Limit of proportionality

Point beyond which stress is no longer directly proportional to strain, Hooke’s law stops applying

Ultimate Tensile Stress

Maximum stress an object can withstand before breaking

Breaking point

Strain at which an object breaks

Ductile Material

A material with a big plastic region

Brittle Material

A material with a small plastic region

Yield point

Point beyond which a small increase in stress causes a large increase in strain

Extension of springs in series

x total= xa + xb

Force on springs in series

Ftotal= Fa= Fb

Spring constant of springs in series

1/k total= 1/ka + 1/kb

Extension of springs in parallel

xtotal= xa= xb

Force on springs in parallel

Ftotal= Fa + Fb

Spring constant of springs in parallel

ktotal= ka+ kb